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# Piece: https://leibnizlegible.com/api/records/985/text
# Catalogue record: 985 — [Aufz. zu Differentialgleichungen]
# Incipit: ∫[[10dy+yd10+dy]/[10y+11]] + 13y + 14 = 0 et differentiando
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=985&katnr=58567
# Work: https://leibnizlegible.com/work/00068051
# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 6
# Folios: Bl. 23 (from the shelfmark LH 35, 6, 6 Bl. 23): 2 pages, canvases 45–46, page ids 00068051:0045 to 00068051:0046
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068051&page=45
# Lines: 151 recognised on 2 of 2 pages, mean confidence 0.77
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 23r — 00068051:0045
# Source image: https://digitale-sammlungen.gwlb.de/content/00068051/jpgs/default/00000045.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 74 lines, status machine
C
dis
(iody + yd1o+g
10y  + 1
Cdu
et differentiando 10 dus +ydiot
0=
10y+1
Hal
Het + 10 dy +y d10 + 11d14 + 10. 139dy + 10dByy
1131387 + y 1d 13 d11
2y 10d14
20 dy +21y
in tod1Z in
a
10 A13
24
in10d13
24
10. 13 = 10 d13023 :29
11 = (R 10 20d 13 - 24: 13+24. Ex dy
seu cquendio 11 = h10
es
23ydy +
et sit
24y7
10d13
24
d13: 13 = 24: 28 et habetur 13
Ergo ex y fit duo + 10 hd 13+10d. 4 2od3
ud 4 = hio d14 = 22. 10d13: 24 - det hd1o- 10dh
Ergo ex y fit d1o + 10h d13 + 22. 10d13: 24h - deo = 10dh: h
Et habetur 10.
Resumamus integum calculum
Unde tandem habetur et diae per
(m ly +ydmtadn + Py +
M y +a
maga yam + adn-: mytan
aa
=
Et differentiando fit
+pdy: ac + dp g:aa + dq: a
en a du + aadm y t maxyy
nandque + an dp 1
a am dqe
Abbndp + Cmap
mapyy
+aamdus
anp 4y
fndp
a
+mpydy
+gmapj a
Ex yay sict fet dp: ∞ a:9 et habetur P logarithmice
8 Mp
seu comnpendio n = hm: a et du  ham: a + dE. m:9
Rursus Ex
et ex y fist a ham + aodhm + ansuse m bb dp m. ubi prr amdus su
et andus = Cmdp = aadm - Am dp. Ergo ex 5 et 6. fiet
pers
ham taadhm + chmap(= aah dm= hh map = bb dpm
sed ita evanescit m
sin ydys L yydm +ncly y an + aa dp + Q seu imytus + hyem +
nec quicquam lurramur
eu sic:
myus faru = aap
14
= mdq y)
+ 139 +14 =0
10du +go u
l pelidus ndit athaya)uq
ingti
in 1odi2
s

## Folio 23v — 00068051:0046
# Source image: https://digitale-sammlungen.gwlb.de/content/00068051/jpgs/default/00000046.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 77 lines, status machine
M
e
a
eb
yrqu+ a: a
F s tat C0
 May + anG +adm = my +an
pydus +taqdy tpesy tacdqus y + afar = adt
d= S
de b + b hdeo b = d5. seu co = ds = 5.
d
en h
fit ds: 5 = dh  + erhdco
seu hds = dh + hedeo
it h = 10y +11 (= 20y+21 co-
dh = cody + Gdco rdu Y df 2edy r 1) d2o, 121
dh +hdeo
has-
de 2
 307 +34
deo = 23 30dy + d3o Y + d3)
 1d21 + ad20y + 11. 20 dy 10d20 yy (+ 10. 20y dy)
+10 del.
11.21 dio 2y
1d31
du. 20
11d20
1003
10.2d.
Il3ody
5dh
23
aeo. 2077
10d0 yy
10.309 1030fy 1030C dy 1030byy
. Cogay
+0. 2oydy)
103oycy
1030 y dy
si 10 et 20 sut constantes, habetur 30 per yui
per duaI= 2) per I1 simpliciter cognite integre ex
ex
Epconaliter
Et tollendo d3) per y et Y. sit relatuo in qua 11. H et X 1 dye
E)
it
a
ytah + 1
2
reter (meya ydm f adn: my-ato +
myran
L mytan gdys tydus tach
frelgytan may+ gam tad
ammodue +amdm gy + aamdny + aamndue += +a ndn ) (ammdus +semm  + anC y tamipa
q
amuydy tandgyus aangmus
amny
aana dy
O
ang) dy) admus yy tandu y - a tm dy
qmmyus
qy
am
anth
+
aegon y
b fon astnn. Ex 716
sb= sam: m  ag: n
=ahdn CErgo g = msb: a = m.
Et Exdus sit aama+ ansist- ansisamim an an
am hic vala iptius h substituatur in e sent muma y. pent
+igmanus   anen aendte tahnb+ 5b n P. antm: m _asman-asim- ant
anan L ansbana anstum: in duamfdri
a
X10gb = y
axlyb.. 1
av = v